Answer the following problems and provide the solution:

1. A hospital found out that there is a higher incidence of food poisoning in adults than in children. Thirty-four of the 250 adults and 16 of 275 children were food poisoned according to the hospital survey. Determine if there is enough evidence to believe the hospital claim. Use a 2.5% significance level.

2. In a small grocery, 23% of the bottled products were sold while 63% of the canned goods were not. If there were 345 bottled products and 330 canned goods, is there a significant difference between the proportion of sales of bottled products and canned goods? Test at 0.01 level of significance.